Definition

A polynomial is the algebraic sum of more monomials. It contains only constants (numbers) and variables using only addition, subtraction and multiplication.
Example of polynomials
e The second polynomial is NOT normal form because it has like terms that must be added, so it becomes:

A polynomial is in normal form if like terms have been added and deleted monomial null.

Grade

The degree of a polynomial is the maximum degree of the monomials that compose it. The above polynomials can have all 2 .
A polynomial is homogeneous if all the monomials that compose it have the same degree.

This polynomial is homogeneous of degree 2.

Sum

The sum or product of two polynomials is always a polynomial.

The sum of two polynomials is a polynomial that contains all monomials of the two polynomials and should be reduced to normal form by adding the like terms. Example:

The subtraction of two polynomials is changing all the signs of the monomials that belong to the polynomial with the minus sign in front. Example

In the online skills is calculated once the sum (without the intermediate step where you change the sign).

Product

The product of polynomial is obtained by applying all the associative property, commutative and distributive, that every monomial of the polynomial must first be multiplied for each monomial of the second polynomial. Example.